Geodesic
Finiteness of the set of automaton Post bases with a decidable completeness problem
Diskretnaya Matematika, Tome 10 (1998) no. 3, pp. 57-63.

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The bases under consideration are those of the form $M=\Phi\cup\nu$, where $\Phi$ is a Post class and $\nu$ is a finite system of automaton functions. It is shown that the sets of Post classes $\Phi$ for which the completeness problem for $\Phi\cup\nu$ is solvable, respectively, the $A$-completeness problem for $\Phi\cup\nu$ is solvable, are finite. 
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     author = {D. N. Babin},
     title = {Finiteness of the set of automaton {Post} bases with a decidable completeness problem},
     journal = {Diskretnaya Matematika},
     pages = {57--63},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1998_10_3_a4/}
}
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D. N. Babin. Finiteness of the set of automaton Post bases with a decidable completeness problem. Diskretnaya Matematika, Tome 10 (1998) no. 3, pp. 57-63. http://geodesic.mathdoc.fr/item/DM_1998_10_3_a4/